Synthetic images for a magnetic resonance imaging scanner using linear combinations of source images

ABSTRACT

The invention consists of three image-postprocessing phases for the purposes of generating high-quality quantitative MR images (proton density (PD), T 1 , and T 2 ) as well as high-quality virtual MR images with continuously adjustable computer-synthesized contrast weightings, from source images acquired directly with an MRI scanner. Each of the image-postprocessing phases uses one or several new computer algorithms that improve image quality with respect to prior art, including linear-combination-of source-images (LCSI) algorithms for generating PD images and model-conforming algorithms for generating Q-MR images of tissue properties that influence NMR relaxation.

RELATED APPLICATIONS

This Application for United States patent is filed as a DivisionalApplication of the parent U.S. patent application Ser. No. 09/779,770filed on Feb. 8, 2001, now issued as U.S. Pat. No. 6,823,205 B1 on Nov.23, 2004.

Co-pending, and terminally disclaimed Allowed U.S. patent applicationSer. No. 10/794,924 filed on Mar. 5, 2004, which has not yet issued, isalso a divisional of parent U.S. patent application Ser. No. 09/779,770filed on Feb. 8, 2001, which issued as U.S. Pat. No. 6,823,205 B1 Nov.23, 2004.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to magnetic resonance imaging (MR imaging), andmore particularly to computing quantitative images as well as syntheticimages from scan data, with the purpose of allowing the user to performvirtual MRI scanning retrospectively and not requiring the presence ofthe patient.

2. Background Information

In magnetic resonance image scanning (MRI scanning), images of asubject, usually a patient's body, are produced through the interactionof a magnetic field applied to the patient's body and the magneticmoment of protons. Each proton behaves as small bar magnet, and thestrength of the bar magnet is referred to as the “magnetic moment” ofthe proton. All protons have the same value of magnetic moment, just aseach proton has the same value of electric charge. The protons are thenuclei of hydrogen atoms. The hydrogen is chemically bonded in compoundsof the patient's tissue.

It is standard engineering practice in MRI imaging to apply a strongmagnetic field substantially parallel to the spinal column of thepatient. This magnetic field is referred to as the “longitudinalmagnetic field” and is represented in symbols as B0. Upon theapplication of the longitudinal magnetic field, protons in the patient'stissue align with the magnetic field to produce a magnetization(longitudinal magnetization) of the patient's tissue. The longitudinalmagnetization is a vector quantity that points along the appliedlongitudinal magnetic field. The magnetization of the patient's tissuemay be represented as formed by many protons aligned with thelongitudinal magnetic field.

The patient's magnetization is used to produce images by observing itsresponse to a magnetic field applied by radio frequency pulses, wherethe radio frequency magnetic field is applied perpendicular to thelongitudinal magnetic field. The frequency of the radio frequencymagnetic field is chosen, along with the time duration of theapplication of the radio frequency magnetic field, to cause the protonsto rotate, more precisely to precess, by a desired angle. The angle bywhich the protons rotate, or precess, is referred to as the “flipangle”. Ordinarily, radio frequency magnetic fields are applied torotate the protons through an angle of 180 degrees so that theirmagnetization points in the reverse direction of the appliedlongitudinal magnetic field (that is into the anti-parallel direction),or to rotate the protons through an angle of 90 degrees so that theirmagnetization points into a plane perpendicular to the direction of theapplied longitudinal magnetic field, that is into the “transverseplane”. Other values of the flip angle may also be employed in MRIimaging.

An image reproducing the proton density in the patient's body may beobtained by applying a radio frequency field for a time sufficient torotate the proton magnetization through to a 90-degree angle, and suchan application of a radio frequency magnetic field is referred to asapplying a “90 degree” RF pulse. Upon application of a 90 degree RFpulse, the protons are rotated from a direction substantially parallelto the longitudinal magnetic field into a direction substantiallyperpendicular to the longitudinal magnetic field. The proton magneticmoments, during this rotation, remain substantially aligned with eachother, so the patient magnetization becomes a vector in the planeperpendicular to the longitudinal magnetic field. The planeperpendicular to the longitudinal magnetic field is referred to as the“transverse plane”.

The patient's magnetization in the transverse plane is substantiallyequal in magnitude to the value that it had before application of the 90degree RF pulse, however the patient's magnetization points in adirection in the transverse plane. For example, the transverse plane canbe described with an X-axis and a Y-axis, and the X-axis may be chosenso that it is aligned with the magnetization in the transverse plane atthe end of the 90-degree RF pulse. The magnetization in the transverseplane rotates in the transverse plane, and as a consequence of thisrotation generates a radio frequency signal originating from thepatient's tissue. This radio frequency signal is detected by a radioreceiver, and is analyzed to produce an image.

A particular transverse plane is chosen for readout by applying alongitudinal magnetic field gradient, and choosing the frequency of theRF pulse to resonate with the protons in the chosen transverse plane.Ordinarily, changing the frequency of the RF pulse while longitudinalmagnetic field gradient is held constant shifts the position of thedesired transverse plane. The radio receiver receives the RF signalgenerated by the rotating magnetization, and the RF signal received bythe radio receiver is spread over a frequency band, and with differentphases, by the application of two transverse magnetic field gradients.For example, a transverse magnetic field gradient is applied, and a readout of emissions from the patient's tissue is obtained from the RFreceiver. Again, a different transverse magnetic field gradient isapplied, and a second readout is obtained from the RF receiver. Asequence of readouts is obtained, for different radio frequency valuesand for different phases, by applying different magnetic fieldgradients. A Fourier transform of the frequency and phase informationreceived by the RF receiver is then computed. The output of the Fouriertransform calculation produces the image of the patient's tissue. Theimage is presented as a two dimensional matrix of pixels.

After a first image is obtained, a waiting period is introduced. At theend of the waiting period a second image of the patient's tissue in thesame transverse plane is obtained. The intensity of the radio frequencysignal generated by the patient's tissue is reduced in the second imagein comparison with the strength produced in the first image bytransverse relaxation phenomena. Transverse relaxation phenomena aremodeled by a transverse relaxation time, referred to as “T2”. Thisreduction in the signal in the second image is used to compute thetransverse relaxation time T2. The values of T2 may be computed at eachpixel of the image.

Transverse relaxation phenomena, which are measured by the measuredvalue of T2, are predominately caused by different protons in thetransverse plane being subject to slightly different magnetic fields.The different magnetic fields throughout the transverse plane have theirorigin in several phenomena: the first being the magnetic field gradientwhich is intentionally applied to the transverse plane in order toobtain space resolution in the transverse plane; a second beingdifferent chemical environments of the protons in molecules withindifferent regions of the transverse plane; and a third being movement ofthe protons through the tissue of the patient, such as caused by bloodflow, etc.

Additionally, the protons in the transverse plane relax back to beingparallel to the longitudinal magnetic field with a relaxation timereferred to as “T1”, where T1 is known as the “longitudinal relaxationtime”.

A 180-degree RF pulse may be applied to the patient's tissue. The resultof the 180-degree RF pulse is that the proton magnetic moments arerotated 180 degrees. This rotation points the protons away from beingparallel to the longitudinal magnetic field to being anti-parallel. Theprotons then relax toward the parallel orientation of the longitudinalmagnetic field with the transverse relaxation time “T1”. After a waitingtime from the 180-degree pulse, a 90-degree RF pulse is then applied tothe patient's tissue. The 90-degree RF pulse causes the netmagnetization of the patient's tissue to rotate 90 degrees into thetransverse plane where the magnetization precesses, and so produces anoutput RF signal from the patient's tissue. An image is again read outby using transverse magnetic field gradients and the RF receiver.

It is standard engineering practice to use a sequence of 180-degree RFpulses and 90-degree RF pulses in order to generate desired images by anMRI imaging apparatus.

In describing images of a patient's body taken by MRI imaging, it isnecessary to introduce some additional geometric terminology. Thepatient's body is regarded as being made of slices, where the slices arein the transverse plane, that is in planes perpendicular to thelongitudinal direction. The slices have thickness in the longitudinaldimension, for example a thickness of 0.5 millimeter, 1 millimeter, 2millimeters, etc. (hereinafter millimeters will be abbreviated by “mm”).An “x” and “y” axis are defined as fixed in the patient's body, and the“x” and “y” axes lie in a transverse plane, where a “z” axis isintroduced as lying along the longitudinal axis and parallel to theapplied longitudinal magnetic field. Each of the slices is divided bylines parallel to the patient's “x” and “y” axes to form smallrectangular parallelepiped elements of patient's tissue referred to as“voxels”. A voxel is a small volume element of patient's tissue. Thevalues of observed quantities in voxels are presented as atwo-dimensional image, where each element in the two dimensional imageis referred to as a “pixel”. Quantities, which may be observed in avoxel during MRI imaging, are: proton density; value of transverserelaxation time T2 in the voxel; value of longitudinal relaxation timeT1 in the voxel, etc. The values of the quantities observed in a voxelare then presented as a two dimensional image of pixels, where the imageis usually presented on a computer screen where it may be photographed,printed by a computer printer, etc.

For example, an analysis of two images following a 90-degree RF pulseyields a value of the transverse relaxation time T2. For example, afterapplication of the 90 degree RF pulse, a waiting time, referred to as“TE1” is observed. After the waiting time TE1 is observed, a readout ofan image is obtained. After a further waiting time referred to as “TE2”,a second image is obtained.

When a 90 degree RF pulse is applied to a patient, the first image thatis taken after the TE1 waiting time is referred to as a proton densityweighted image, a “PD weighted” image. The terminology “PD weightedimage” is used because this is the first image in a sequence, and theintensity of the image in each voxel of the image is regarded as beingproportional to the proton density in the corresponding voxel of thepatient's transverse plane. The two-dimensional image of pixelsgenerated from the intensity of the signal observed in the voxels isthen presented on a computer screen, etc.

The second image produced after the TE2 waiting time is referred to as a“T2 weighted” image. The terminology “T2 weighted” image is used becausethe image is reduced in intensity at each voxel because of transverserelaxation processes, and so is dependent upon the value of T2 at eachvoxel of the transverse plane.

When a 180-degree RF pulse is applied to a patient, the longitudinalmagnetization is rotated to an anti-parallel direction to the appliedlongitudinal magnetic field, and then the longitudinal magnetizationbegins relaxing back to the parallel direction with the relaxation timeof T1. The value of T1 at each voxel may be determined by a sequence ofimages. Ordinarily the images to determine T1 are taken by: first,applying the 180 degree RF pulse to obtain anti-parallel orientation ofthe patient's longitudinal magnetization; second, by applying a 90degree RF pulse after a longitudinal waiting time of invT from the 180degree RF pulse to rotate the longitudinal magnetization into thetransverse plane; and third by taking one or more subsequent images inorder to obtain the value of T2 at each voxel of the slice. Images takenafter at least two different values of longitudinal waiting time invTmay then be analyzed to obtain a value of T1 at each voxel. These twoimages will be of different intensity because of the recovery oflongitudinal magnetization caused by the longitudinal relaxationprocesses modeled by the longitudinal relaxation time T1. And the valueof T1 may be different in each voxel, giving rise to images havingdifferent contrast information at the different values of waiting timeinvT.

It is standard engineering practice to take the images to determine T1by the additional steps of: first applying a 90 degree RF pulse afterthe waiting time of invT from the 180 degree RF pulse to rotate thelongitudinal magnetization into the transverse plane, and then taking animage after a waiting time of TE1, and a second image after anadditional waiting time of TE2 , where these values of TE1 and TE2 arethe same as the waiting times for taking an image after an isolated 90degree RF pulse. The images taken after an isolated 90 degree RF pulse,and after a 180 degree pulse followed by a 90 degree RF pulse, may thenbe combined in an analysis to obtain values of T1 and T2 at each voxelof the patient's body.

It is a standard clinical and engineering terminology to refer to: thefirst image after a 90 degree RF pulse as a “PD weighted” image (protondensity image); the second image after a 90 degree RF pulse as a “T2weighted” image; the first image after a 180 degree RF pulse and awaiting time of invT, then followed by a 90 degree pulse, as a “T1weighted” image; and the second image after both the 180 degree RF pulseand the 90 degree RF pulse as a T1-T2 weighted image.

Clinical information is carried in the different images, the PD weightedimage, the T1 weighted image, the T2 weighted image, the T1-T2 weightedimage, and other images produced by a particular choice of RF pulsesequences. In order to produce images by different RF pulse sequences,it is necessary to place the patient in the MRI imaging scanner and tosubject the patient to the desired sequence of RF pulses.

There is needed a way to improve the images obtained from the radioreceiver data, so that clinical information may be obtained withoutregard to the sequence of RF pulses applied to the patient's tissue.

SUMMARY OF THE INVENTION

The invention consists of three image-postprocessing phases for thepurposes of generating high-quality quantitative MR images (protondensity (PD), T1, and T2) as well as high-quality virtual MR images withcontinuously adjustable computer-synthesized contrast weightings, fromsource images acquired directly with an MRI scanner. Each of theimage-postprocessing phases uses one or several new computer algorithmsthat improve image quality with respect to prior art, as described indetail in the following sections of this document.

Specifically, the Image-PostProcessing Phases are:

-   1) Generation of high-quality synthetic proton density images by    computing linear combinations of source images (LCSI algorithms)    that were directly acquired with an MRI scanner. The objective of    this phase is to generate a high-quality computer representation of    the patient for the purpose of virtual MRI scanning, or equivalently    for using this representation as a cybernetic virtual patient. The    source images used as input to the LCSI algorithm(s), which are    directly acquired with the MRI scanner, may include one, several, or    all the images generated with the application of the physical pulse    sequence used to scan the patient. Furthermore, for the purpose of    generating a computer representation of the patient for virtual MRI    scanning, the specific applied MRI pulse sequence(s) as well as the    number or the individual contrast weightings of the source images    per slice generated with it, are not unique. As discussed below in    this patent application, the first phase of the invention (i.e.    generating proton density images as linear combinations of source    images) was applied to source images that were generated with a    pulse sequence known as mixed turbo spin-echo (MIX-TSE) but many    other are possible. The MIX-TSE pulse sequence used here as an    example, produced four images per anatomic slice, specifically: a PD    weighted image, a T1 weighted image, a T2 weighted image, and a    combination T1-T2 weighted image. The values of the coefficients for    the LCSI algorithms are also not uniquely defined. These values are    chosen first and foremost so as to produce accurate representations    of the proton density spatial distribution within the slice and    second, so as to maximize the signal-to-noise-ratio (SNR) of the    generated image. Two exemplary sets of LCSI algorithms are discussed    in this document: 1) LCSI-basic: consist of a simple set of linear    coefficients that uses solely the source image that is closest to    the proton density image, and 2) LCSI-maximum-SNR: consists of a set    of coefficients obtained by means of an optimization algorithm to    maximize signal to noise ratio, SNR, which uses all source images (4    in the case of this example). Once the values of the LCSI    coefficients are chosen, LCSI proton density images (LCSI_LPD) are    calculated at every location of patient that was physically scanned    with the MIX-TSE pulse sequence.-   2) In the second phase of the invention, the values of longitudinal    relaxation time T1 and transverse relaxation time T2 are computed at    each scanned voxel of the patient using also the source images and    by means of what will be referred to hereafter as model-conforming    quantitative algorithms. The defining feature of model-conforming    Q-MRI algorithms is that these are based on a physics model of    tissue magnetism that is conditioned in response to    signal-to-noise-ratio criteria in the source images. Specifically,    in the model conforming algorithms the pixel values of the input    source images are first compared to the noise level in the image,    then, if these pixel values exceed the noise level the physics model    applies, otherwise a predefined value for the output (T1 and T2)    results. The use of model conforming algorithms is shown to reduce    the incidence of inaccurate pixel values in Q-MR images as well as    in synthetic images produces by virtual MRI scanning.-   3. In the third phase of the invention, the values of the    LCSI-proton density, T1, and T2 obtained for each voxel are then    used to compute a synthetic MR image with computer-generated    contrast weighting. In this phase, synthetic images representing any    imaginable sequence of pulses may be computed. Also, the voxels may    be rearranged to give slices through the patient's body at any    desired orientation, for example slices parallel to the transverse    plane, slices parallel to the longitudinal axis, and slices at any    desired angle to the longitudinal axis and the transverse plane.

In summary, the quality—high SNR, negligible incidence of pixel dropoutartifacts, and continuously adjustable contrast weightings—of thesynthetic images produced with the algorithms of this invention, isconsistently superior to that produced by prior art. These image qualityimprovements result primarily from using LCSI_PD images as the virtualpatient, and secondarily from using model-conforming Q-MR images (e.g.T1 and T2) to produce contrast weighting in virtual MRI scanning.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention description below refers to the accompanying drawings, ofwhich:

FIG. 1 is; a plan diagram of a patient in a MRI scanner;

FIG. 2A is; is a timing diagram showing a sequence of scanning events;

FIG. 2B is a graph showing the time dependence of longitudinalmagnetization;

FIG. 3 is a flow chart in accordance with the invention;

FIG. 4 is a flow chart illustrating the prior art;

FIG. 5 is an IR_E1 source image, T1 weighted;

FIG. 6 is an IR1_E2 source image, T1 & T2 weighted;

FIG. 7 is an IR2_E1 source image, PD weighted;

FIG. 8 is an IR2_E2 source image, T2 weighted;

FIG. 9 is a synthetic image, an axial orthogonal reconstruction;

FIG. 10 is a synthetic image, a saggital orthogonal reconstruction;

FIG. 11A-FIG. 11H is a sequence of synthetic images for varying valuesof longitudinal waiting time; and,

FIG. 12A-FIG. 11H is a sequence of synthetic images for varying valuesof spin echo waiting time.

FIG. 13 is a block diagram of a physical-virtual MRI scanner with aconnection to a computer network

DETAILED DESCRIPTION OF AN ILLUSTRATIVE EMBODIMENT

Image Acquisition

MRI Scanner

Turning now to FIG. 1, an MRI scanner 100 with a patient 102 is shown.Patient 102 is shown having his head 104 positioned within thelongitudinal magnetic field coil 106. Coordinate axes 110 have a z-axis112 along the axis of longitudinal magnetic field coil 106, and anx-axis 114 and a y-axis 116 in a transverse plane. A transverse plane isperpendicular to the axis of the longitudinal magnetic field coil 106.The longitudinal magnetic field coil 106 generates a longitudinalmagnetic field B0 120. The direction of longitudinal magnetic field B0120 is along the axis of the longitudinal magnetic field coil 106, thatis along the z-axis 112.

Longitudinal gradient magnetic field coil 130A and 130B are connected soas to produce a magnetic field gradient along the z-axis 112, so thatthe value of the longitudinal magnetic field 120 at the location of adesired transverse slice (not shown in FIG. 1) of the patient's bodywill have a desired value.

An x-axis magnetic field gradient coil 140A is shown, and the outline ofthe patient through the x-axis magnetic field gradient coil 140A isshown through the block representing the x-axis magnetic field gradientcoil 140A. A matching x-axis magnetic field gradient coil is locatedbehind the patient, is obscured by the x-axis magnetic field coil 140A,and so is not shown in FIG. 1.

A y-axis magnetic field gradient coils 142A and 142B are shown. Incombination, the y-axis magnetic field gradient coils 142A, 142B producea magnetic field gradient along the y-axis.

The z-axis magnetic field gradient coils 130A, 130B are used to select atransverse plane within the patient's body for scanning. The x axismagnetic field gradient coils 140A and the hidden coil which is notshown, in combination with the y axis magnetic field gradient coils 142Aand 142B are used to provide a variation of the magnetic field in theselected transverse plane so that radio frequency signals may bereceived from the transverse plane, and an image of that transverseplane within the patient may be reconstructed from the received radiofrequency signals.

Radio frequency transmitting coil 150 receives radio frequency energyfrom a transmitter, as shown in FIG. 13, and emits radio frequencyradiation which is absorbed by patient 102. Radio frequency receivingcoil 152 receives the radio frequency emissions from the magnetizationof the protons in the patient's 102 tissue.

Generation of images is thoroughly discussed by P. Mansfield and P. G.Morris in their book NMR Imaging in Biomedicine, published by AcademicPress in 1982, all disclosures of which are incorporated herein byreference.

Mixed Turbo Spin-Echo Pulse Sequence

Turning now to FIG. 2A, a timing diagram 200 for a sequence of events inoperation of a MRI imaging scanner is shown. Time axis 202 is shown withtime arrow 204. The first event shown, at time 210, is the applicationof a 180-degree RF pulse to the patient. After a waiting time of “invT”212, at time 214 a 90-degree RF pulse is applied to the patient. Thewaiting time invT 212 is often referred to as the “inversion waitingtime”.

A first image is acquired at time 226, and a second image is acquired attime 236. The terminology for these images is that they are longitudinalrelaxation images, or IR images, and they are E images, referring to thespin echo method of image acquisition, as shown by label 216. The imagesare IR images because of the initial 180 degree RF pulse applied at time210 turned the patient's magnetization in the selected transverse sliceinto anti-parallel to the longitudinal magnetic field B0 120, and thewaiting time invT 212 until time 214, when the 90 degree RF pulse wasapplied, after the patient's magnetization had an opportunity to relaxduring the waiting time invT back toward the parallel direction to thelongitudinal magnetic field B0 120.

After a waiting time of TE1 220 a sequence of spin echo data acquisitionevents using a variety of transverse magnetic field gradients isacquired by the MRI imaging scanner, as shown by the vertical lines 222.The data acquisition events 222 produce an image, after Fouriertransform treatment of the data, to produce an image referred to as theIR_E1 image. Label 224 indicates that vertical lines 222 are referred toas a “spin echo (SE) readout #1”. The image is referred to as beingproduced at time 226, although the image is acquired during the timeinterval represented by the vertical lines 222.

After a further waiting time TE2 230 another set of spin echo images areacquired by the MRI imaging scanner, as indicated by the vertical lines232. Again, the sequence of spin echo readouts represented by thevertical lines 232 are used to generate an image, after Fouriertransform treatment of the data, to produce a spin echo readout labeledas “SE-readout #2” 234. The image obtained through the spin echoreadouts “SE-readout #2” 234 is referred to as the IR_E2 image, and itis referred to as being acquired at time 236. The IR_E2 image isdegraded from the earlier IR_E1 image, mainly by transverse relaxationprocesses, as the waiting time TE2 230 is short in comparison with thetransverse relaxation time T1.

Typical values in an exemplary embodiment of the invention for thevarious physical parameters discussed are listed in Table 1 below:

TABLE 1 gives Pulse sequence parameters MIX-TSE used for brain imagingParameters MIX-TSE Settings for brain scans Geometry Field of view 220mm (rectangular 70%) Matrix-FE direction 256 Matrix-PE direction 143Imaging plane Coronal PE direction Left-right Slice thickness 2.5 mmNumber of slices  80 Inter-slice gap 0 mm Contrast Flip angle: FA 90°First echo: TE1eff 8 ms (centric profile order) Second echo: TE2eff 113ms (linear profile order) Turbo factor: TF 18 (9 per echo) Echo spacing:ES 8 ms Inversion time: invT 700 ms TR_(SE) 8721 ms TR_(IR) 9421 msOther Scan time 10:16 (minutes) SAR 3.1 Watts/kg

In Table 1, the parameters are grouped according to separate categoriesthat describe the main practical and technical aspects of the MIX-TSEpulse sequence used in this work. Abbreviations: SAR=specific absorptionrate, FE=frequency encoding, PE=phase encoding, SS=slice select,TE1eff=first effective echo time, TE2 eff=second effective echo time.

The time required to complete a complete scan is approximately 10minutes. Power exposure to the patient is approximately 3.1Watts/kilogram.

Observed values of longitudinal relaxation time T1 for tissue rangesfrom about 0.4 seconds to 1.8 seconds. Observed values of transverserelaxation time T2 for tissue range from about 0.02 seconds to 0.21seconds, as given by Mansfield and Morris in their above mentioned bookNMR Imaging in Biomedicine, at pages 17-24. However, the observed valuesdepend upon the tissue, its state of health or disease, and thefrequency of the proton resonance.

Returning now to FIG. 2A, additional image acquisition is shownbeginning at time 250, and after waiting for the time period TR_SE 252(in an exemplary embodiment of the invention TR_SE 252 is approximately8.7 seconds). It is assumed that during the waiting period TR_SE 252 thepatient's tissue loses all memory of the earlier pulse sequencesbeginning at time 210. A 90-degree RF pulse is applied to the patient'stissue at time 250. After a waiting time of TE1 254 an image is acquiredat time 256, as shown by the vertical lines 258 indicating spin echoevents, and label 260. Label 260 indicates that the image acquired attime 256 is referred to as the IR2_E1 image.

After an additional waiting time TE2 270 another image is acquired attime 272, as indicated by the vertical lines 274 indicating spin echoevents. As shown by label 276, the image acquired at time 272 isreferred to as the IR2_E2 image.

Another sequence of imaging events may then begin at time 280, after awaiting time of TR 282.

In an exemplary embodiment of the invention, TR 282 may be approximately9.5 seconds.

The pulse sequence shown in FIG. 2A is used in this exemplary embodimentof the invention as it easily can be obtained with a Philips MRI Scanner(Gyroscan ACS-NT, Philips Medical Systems, Shelton Conn.) and thisscanner was used to obtain the data shown herein below.

The pulse sequence shown in FIG. 2A is referred to as the “MIX-TSE”pulse sequence, meaning that the pulse sequence produces a mix of a PDimage, a T1 weighted image, a T2 weighted image, and a T1-T2 weightedimage.

Turning now to FIG. 2B, the behavior of the longitudinal magnetizationof the patient's tissue is shown by the graphs 290. Just before time 210the magnetization of the patient's tissue is substantially parallel tothe applied magnetic field B0 120, the longitudinal magnetization. Thelongitudinal magnetization is given the representative value of +1.0 ata time just before time 210.

At time 210 the 180-degree RF pulse is applied by scanner 100 to thepatient's tissues. The value of the magnetization, plotted along thevertical axis 292, is driven from a value of +1.0 to a negative value of−1.0, as shown at time 210. This change in the patient's magnetizationis brought about as a result of the spin axis of the protons incompounds in the patient's tissue being caused to precess, or rotate, by180 degrees by the 180 degree RF pulse applied at time 210.

Curves for different values of longitudinal relaxation time T1 areshown, curve 291A has a small value of T1, curve 291B has a larger valueof T1, curve 291C has a still larger value of T1, and curve 291D has thelargest value of T1 shown in graphs 290. Each curve represents differenttissue types, each tissue type having its characteristic value oflongitudinal relaxation time T1. The smaller the value of T1, the fasterthe magnetization relaxes back to parallel to the applied magneticfield, and the larger the value of T1, the longer it takes themagnetization of the tissue to relax back to parallel to the appliedmagnetic field B0 120.

After a waiting time of invT 212 90 degree RF pulse is applied at time214. The longitudinal magnetization is driven to zero, as shown by thegraphs, by the application of the 90-degree flip angle RF pulse. Thelongitudinal magnetization is driven to zero by the magnetization beingre-oriented into the transverse plane. The magnetization begins to relaxback from the transverse plane rapidly, “rapidly” because the transverserelaxation time T2 is normally much smaller than the longitudinalrelaxation time T1.

During the waiting time TR_SE 252 the spin echo readouts at time 226 andtime 236 are acquired, without affecting the longitudinal magnetization,as shown by the smooth nature of the graphs 291A-291C during this timespan.

By time 250, after the waiting time TR_SE 252, the longitudinalmagnetization has relaxed back so that the tissue with the slowestrelaxation time (largest value of T1) has relaxed back to the value of+1.0, as shown by the graphs at time 250. The value of +1.0 indicatesthat all protons have regained a spin axis alignment parallel to theapplied magnetic field B0 120.

At time 250 a second 90-degree RF pulse is applied to the patient'stissue by the scanner 100. Again, as at time 214, the longitudinalmagnetization is driven to zero at time 250 as the magnetization rotatesinto the transverse plane. The longitudinal magnetization then begins torelax back to parallel to the applied magnetic field, so that by time280 the tissue magnetization has relaxed back to a parallel orientationto the applied magnetic field B0 120. At time 256 and time 272 the spinecho image readouts are acquired, without substantially disturbing thelongitudinal magnetization as is shown by the smooth nature of thelongitudinal magnetization curves at these times.

Analysis of Images

Theoretical Background

A quantity that decreases exponentially during time may be analyzed byuse of the following equation: $\begin{matrix}{{Y(t)} = {{Y\left( {t = 0} \right)}{\exp\left\lbrack {- \frac{t}{TC}} \right\rbrack}}} & \left\lbrack {{Eq}.\quad 1} \right\rbrack\end{matrix}$Where the symbols have the meaning:

-   the variable t represents time;-   Y(t) represents the value of a quantity Y at time t;-   Y(t=0) represents the value of the quantity at the zero point of    time, where t=0 is chosen for convenience;-   exp is the exponential function;-   TC is the time constant, and is the time for the quantity Y to    decrease in value by an amount of 1/e.

An analysis to calculate TC from measured values of Y at time t=0 and attime t=TM, the measurement time, is given by rearranging equation 1 intothe following equation: $\begin{matrix}{{TC} = {\ln\left\lbrack \frac{Y\left( {t = 0} \right)}{Y\left( {t = {TM}} \right)} \right\rbrack}} & \left\lbrack {{Eq}.\quad 2} \right\rbrack\end{matrix}$“ln” represents the natural logarithm.

The values of the longitudinal relaxation time T1 and the transverserelaxation time T2 are computed using an analysis similar to equation 2at each voxel of a slice of patient tissue, as described in more detailhereinbelow. Each voxel of patient tissue is represented in an image asa pixel, and so from image data the computation is done at each pixel ofthe image.

Linear Combination of Source Images (LCSI)

A composite image is computed from the source images (SI^(m): m=1, . . .N) acquired with the MRI scanner as: $\begin{matrix}{{LCSI\_ PD}_{({i,j})} = {{modulus}\left\lbrack {\sum\limits_{m = 1}^{N}{a_{m}{SI}_{({i,j})}^{m}}} \right\rbrack}} & \left\lbrack {{Eq}.\quad 3} \right\rbrack\end{matrix}$The modulus operation is used since the original source images generatedby the scanner are complex-valued and N denotes the total number ofacquired source images. The symbol LCSI stands for the LinearCombination of Source Images and the symbol SI_((i,j)) ^(m) representsthe pixel at position (ij) of the m^(th) source image acquired from apatient using a selected pulse sequence. The PD in the symbol LCSI_PDindicates that a proton density image is being computed. The symbols(i,j) stand for the calculation being performed at each pixel of theimage, as the pixels are accessed by the integer coordinates “i” and“j”. The symbols α_(m) are coefficients of the linear combination, andare chosen to achieve a desired result in the composite image. Forexample, in an exemplary embodiment of the invention, the values ofa_(m) are chosen to maximize the signal-to-noise ratio in the compositeproton density image.

In an exemplary embodiment of the invention, the sequence of pulsesdescribed through FIG. 2A are used to generate four (N=4 ) images,referred to as the IR1_E1 image 224, the IR1_E2 image 234, the IR2_E1image 258, and the IR2_E2 image 276. With this notation Eq. 2 becomes:LCSI _(—) PD _((i,j))==modulus[a ₁ IR 2 _(—) E 1 _((i,j)) +a ₂ IR 2 _(—)E 2 _((i,j)) +a ₃ IR 1 _(—) E 1 _((i,j)) +a ₄ IR 1 _(—) E 2_((i,j))]  [Eq. 4]Since by definition the LCSI operation is linear in the mathematicalsense, the concept of performing weighted sums of source images for thegeneration of PD images is also applicable in the Fourier domain ork-space in which the primary MR image data kspace_SI^(m) is acquired.The LCSI formula applicable to the primary k-space source images is:$\begin{matrix}{{LCSI\_ PD}_{({i,j})} = {{modulus}\left\lbrack {\sum\limits_{m = 1}^{N}{a_{m}{inv2DFT}\left\{ {kspace\_ SI}_{({i,j})}^{m} \right\}}} \right\rbrack}} & \left\lbrack {{Eq}.\quad 5} \right\rbrack\end{matrix}$In this equation inv2DFT represents the inverse two-dimensional discreteFourier transform operation applied to the primary unprocessed MR imagedata (kspace_SI^(m)) for m^(th) source image in k-space. Furthermore,the LCSI algorithm can also be applied to any of the intermediate statesof the image data, for example the hybrid k-space-image space data stateinv1 DFT {kspace_SI^(m)} that results from a one-dimensional inverseFourier transform. In this case, the LCSI formula is: $\begin{matrix}{{LCSI\_ PD}_{({i,j})} = {{modulus}\left\lbrack {\sum\limits_{m = 1}^{N}{a_{m}\left\{ {{inv1DFT}\left\{ {kspace\_ SI}_{({i,j})}^{m} \right\}} \right\}}} \right\rbrack}} & \left\lbrack {{Eq}.\quad 6} \right\rbrack\end{matrix}$

The next step in the definition of operative LCSI algorithms is todefine specific criteria for adjusting the linear combinationcoefficients a_(m) with the purpose of generating images that arerealistic approximations to the true PD spatial distribution inside thepatient and that at the same time have superior image quality relativeto prior art.

Selection of LCSI Coefficients: Important LCSI Algorithms

Two examples of LCSI algorithms each of which is characterized by aspecific set of linear combination coefficient values {a_(m): m=1, . . ., 4} are of particular practical importance; the first algorithm for itsoverall computational simplicity—hereafter referred to, as LCSI-basicalgorithm—and the second, hereafter referred to, as LCSI-maximum-SNRalgorithm because it makes efficient use of the SNR contained in all thesource images acquired per slice. Since SNR can be traded for higherspatial resolution, this second algorithm is useful for clinicalapplications in which the use of higher spatial resolution scans are ofdiagnostic value.

In the following, these LCSI algorithms are discussed as exemplaryembodiments of the invention.

With the LCSI-basic algorithm, a quantitative PD image is generatedsimply by resealing one source image per slice, specifically that sourceimage the acquisition parameters of which are closest to the acquisitionparameters of an ideal and exact PD image specifically TE=0,TR=infinite, FA=90°, and single slice acquisition. With the MIX-TSEpulse sequence parameters used in an exemplary embodiment of theinvention (see Table 1), the image generated in the third TSEacquisition, that is the first echo of the second IR period (IR2_E1,image 260 of FIG. 2A) is a close approximation to an exact PD image,except for a proportionality normalization factor (Γ) the specific valueof which is chosen such that the pixel values of regions containingsimple fluids (e.g. CSF, synovial fluid, etc.) are numerically equal tounity. Accordingly, the linear combination coefficients for this mostbasic LCSI algorithm are simply {a₁=Γ, a₂=a₃=a₄=0}.

Although the LCSI-basic algorithm is very simple to implement, thegenerated PD images contain information of only one of the source imagesand therefore this algorithm is SNR inefficient. The question arises asto whether some fraction of the SNR that is contained in the othersource images that is IR2_E2 image 276, IR1_E1 image 224, and IR1_E2image 234 can be added constructively to improve the base level SNRprovided by the IR2_E1 image 260 image alone, while preserving orperhaps improving the PD weighted quality of the generated image.Mathematically this problem is equivalent to defining a criterion foradjusting the weighting coefficients so that the relative T1- andT2-weightings of the other three source images IR2_E2 image 276, IR1_E1image 224, and IR1_E2 image 234 balances upon LCSI addition thusgenerating a faithful approximation to a PD image and that has a higherSNR than the IR2_E1 image 260 image alone. Because the second echoes ofthe two IR acquisitions are in the same exponential relation to theirrespective first echoes (i.e. same echo time TE2 , see FIG. 2A), asingle parameter (ξ_(T2)) can be used to control the level of T2contrast in the LCSI image. Furthermore, another single parameter(ξ_(T1)) may be used to control the relative contribution of the twoimages obtained with the two echoes of the IR1 period since these twoimages have the same level of T1-weighting relative to the imagesacquired in the IR2 period. From these considerations a two parameter(ξ_(T1) and ξ_(T2)) LCSI formula, specifically:LCSI _(—) PD _((i,j))==modulus[IR 2 _(—) E 1 _((i,j))+ξ_(T2) IR 2 _(—) E2 _((i,j))+ξ_(T1)(IR 1 _(—) E 1 _((i,j))+ξ_(T2) IR 1 _(—) E 2_((i,j)))]  [Eq. 7]is used as an exemplary embodiment of the invention for the generationof the maximum-SNR PD images for the purpose of virtual MRI scanning.LCSI Maximum-SNR Algorithm: Coefficient Optimization Procedure

As can be expected, the specific optimum values for (ξ_(T1)) and for(ξ_(T2)) depend on the experimental conditions used for imageacquisition. Ranges for these optimum values can be established by meansof the following multi step optimization procedure, the purpose of whichis to attempt reverting the relaxation time weightings of {IR2_E2,IR1_E1, IR1_E2} and then average the resulting three images with IR2_E1.First, as a zero order approximation, the formulas describing therelaxation time weightings of the four images produced by the MIX-TSEpulse sequence can be used to approximately revert the relaxation timeweightings of these. Because the MIX-TSE pulse sequence was implementedwith very long TR_(IR) and TR_(SE) values (see Table 1) these relaxationtime inversion factors are to a very good approximation given by thefollowing equations: $\begin{matrix}{\xi_{T1}^{(0)} = {\frac{1 - {2{\exp\left\lbrack {{- {T1}}/{T1}^{(0)}} \right)}}}{1 - {\exp\left\lbrack {{- \left( {{TR}_{SE} - {TSE}_{shot}} \right)}/{T1}^{(0)}} \right\rbrack}}{\exp\left\lbrack {i\quad\pi} \right\rbrack}}} & \left\lbrack {{Eq}.\quad 8} \right\rbrack \\{{and},} & \quad \\{\xi_{T2}^{(0)} = {{\exp\left\lbrack {{- \left( {{TE2} - {TE1}} \right)}/{T2}^{(0)}} \right\rbrack}{\exp\left\lbrack {i\quad\pi} \right\rbrack}}} & \left\lbrack {{Eq}.\quad 9} \right\rbrack\end{matrix}$

In these equations the complex-valued phase factor represent the 180°out of phase relation between first and second echoes as well as betweenthe IR2_E1 image in relation to the IR1_E1 image. Furthermore, therelaxation times T1 ⁽⁰⁾ and T2 ⁽⁰⁾ represent a non-specific “mediantissue” with intermediate relaxation times within the biologic spectrum.To zero order approximation, by using the values T1 ⁽⁰⁾=800 msec and T2⁽⁰⁾=100 msec, the following values are produced by equations [7] and [8]respectively: ξ_(T1)⁽⁰⁾ = −0.166  and  ξ_(T2)⁽⁰⁾ = −0.350.With these values as starting point, the second step consists incalculating the numerical differences between maximum-SNRimagesgenerated with equation [6] and the IR2_E1 image and determine theranges of (ξ_(T1)) and (ξ_(T2)) values that minimize these differences.The results of such a procedure (column labeled |ΔPD1| in Table 2),which were performed with brain images, show that differences of lessthan 10% between normalized maximum-SNR LCSI images and normalizedIR2_E1 images can be obtained throughout the imaging plane for thefollowing ranges: −0.204≦ξ_(T1)≦−0.097 and −0.122≦ξ_(T2)≦−0.385.Furthermore, in these ranges the SNR improvements were approximatelyfrom 40% to up to 80%. Finally, an approximate absolute minimum for|ΔPD1| was found for ξ_(T1)^((Opt)) = −0.148and ξ_(T2)⁽⁰⁾ = −0.223.These values produce accurate results in the brain as well as in phantomimaging experiments.

TABLE 2 LCSI-maximum-SNR algorithm Median-T1 Median-T2 SNR ^(max-SNR)|ΔPD1| |ΔPD2| msec msec ξ_(T1) ξ_(T2) SNR^(max-SNR) SNR^(IR2) ^(—) ^(E1)Max % Max % 760 90 −0.204 −0.311 49.073 1.778 10.506 112.834 780 90−0.185 −0.311 48.472 1.756 9.911 800 90 −0.166 −0.311 47.86 1.734 9.382820 90 −0.148 −0.311 47.251 1.712 8.902 840 90 −0.131 −0.311 46.655 1.699.044 860 90 −0.114 −0.311 46.068 1.669 9.536 880 90 −0.097 −0.31145.499 1.649 10.241 820 40 −0.148 −0.072 35.533 1.287 13.581 820 50−0.148 −0.122 37.817 1.370 10.324 820 60 −0.148 −0.174 40.296 1.46 8.46820 70 −0.148 −0.223 42.756 1.549 8.256 820 80 −0.148 −0.269 45.0941.634 8.522 820 90 −0.148 −0.311 47.251 1.712 8.902 820 100 −0.148−0.350 49.182 1.782 9.902 820 110 −0.148 −0.385 50.902 1.844 11.187 820120 −0.148 −0.417 52.451 1.9 12.580

A parameter optimization procedure for LCSI-maximum-SNR algorithm isgiven in Table 2. Reference SNR (IR2_E1)=27.6

Model-Conforming Q-MRI Algorithms

The most common artifacts in synthetic MR images, such as pixel dropoutsand the artificial delineation of some tissue interfaces are caused byerrors that can occur in the generation of T1 and T2 Q-MRI images. Theseundesirable effects are most pronounced at locations where the physicalmodel that is assumed in the Q-MRI algorithm is not applicable, forexample pixels representing tissues or materials that do not generate MRsignal, for example cortical bone and air out pixels. Particularly,artifacts are present for pixels representing an admixture ofpartial-volumed tissues with different relaxation properties.

In order to reduce these artifacts, model-conforming Q-MRI algorithmshave been developed, with which quantitative image data is calculatedwith the known MR physics formulas solely for the pixels representingtissues that conform to the physics model assumed in the Q-MRIalgorithm, while for those pixels that do not conform with the model, apredefined fixed value is assigned. Accordingly, with model-conformingQ-MRI algorithms, the pixels that are most problematic and which tend tocause the majority of pixel dropout artifacts, are processeddifferently.

As discussed in the following, the principle underpinningmodel-conforming Q-MRI algorithms is very general and may be applied forthe generation of Q-MRI images of any tissue property (genericallysymbolized by tp) that influences NMR relaxation in that tissue. Thedefining formula for a general model-conforming Q-MRI algorithm thatuses as input any number of the source images {SI^(m), m=1, . . . N forcalculating the value of a generic tissue property tp, evaluated at apixel with coordinates (i, j), can be written in the form of aconditionally-branched set of formulas, with the following structure:$\begin{matrix}{{\left\{ {SI}_{({i,j})}^{m} \right\}\overset{\begin{matrix}{{Model}\text{-}{conforming}} \\{algorithm}\end{matrix}}{\longrightarrow}{tp}_{({i,j})}} = \left\{ \begin{matrix}\vdots \\{{TP}_{\alpha} = {{constant}\overset{if}{\longleftarrow}{\begin{matrix}{{Conditional}\quad{statements}} \\{{based}\quad{on}} \\{{noise}\quad{level}\quad{in}\quad{source}\quad{images}}\end{matrix}}}} \\\vdots \\\vdots \\{{F\left( {SI}_{({i,j})}^{m} \right)}\overset{otherwise}{\longleftarrow}{\begin{matrix}{Formula} \\{{MR}\quad{physics}\quad{model}}\end{matrix}}}\end{matrix} \right.} & \left\lbrack {{Eq}.\quad 10} \right\rbrack\end{matrix}$This formula, which is evaluated on a pixel-by-pixel basis, starts witha number of conditional statements whereby the value of the tissueproperty is assigned to a predefined constant value TP_(α)based on thevalues of the input source images at that specific pixel and in relationto the noise level of the source images that were used as input for themodel-conforming algorithm. The symbol alpha α is an integer thatenumerates the number of the predefined constant used in the algorithm.

Exemplary embodiments of this invention, as applied to the calculationof T1- and T2-Q-MR images, using as input the source images IR1_E1 image224, IR1_E2 image 234 IR2_E1 image 260, and IR2_E2 image 276 that wereacquired with the MIX-TSE pulse sequence discussed above, are describednext.

A model-conforming Q-MRI algorithm used for the generation of T1quantitative images consists of the following operations:$\begin{matrix}{{T1}_{({i,j})} = \left\{ \begin{matrix}{0\overset{if}{\longleftarrow}{\begin{matrix}{{{IR2\_ E1}_{({i,j})}} \leq {noise}} \\{and} \\{{{{{IR1\_ E1}_{({i,j})}} - {{IR2\_ E1}_{({i,j})}}}} \leq {noise}}\end{matrix}}} \\{\frac{TI}{\ln\left\lbrack {\frac{1}{2}\left( {1 - \frac{{IR1\_ E1}_{({i,j})}}{{IR2\_ E1}_{({i,j})}}} \right)} \right\rbrack}\overset{otherwise}{\longleftarrow}{\begin{matrix}{{For}\quad{pixels}\quad\left( {i,j} \right)\quad{where}} \\{{physics}\quad{model}\quad{is}\quad{valid}}\end{matrix}}}\end{matrix} \right.} & \left\lbrack {{Eq}.\quad 11} \right\rbrack\end{matrix}$

In this formula, invT is the inversion time of the MIX-TSE pulsesequence that was used for acquisition of the source images (see Table1).

With this exemplary embodiment of a T1 model-conforming algorithm, thecondition that is used for selecting pixels that do not conform with thesimple physics model of T1 inversion recovery following a 180-degreesinversion pulse, is based on identifying those pixels where nomeasurable signal change is measured at the two different recovery times(i.e. ∥IR2_E1 _((i,j))|−|IR1_E1 _((i,j))∥≦ noise and that also have anoverall signal that is below noise level (|IR2_E1 _((i,j))|≦ noise).Furthermore, for model-conforming pixels, the T1 values are computed bythe simple inversion recovery ratio model as applied to the MIX-TSEpulse sequence, which is${{T1}_{({i,j})} = {{T1}/{\ln\left\lbrack {\frac{1}{2}\left( {1 - \frac{{IR1\_ E1}_{({i,j})}}{{IR2\_ E1}_{({i,j})}}} \right)} \right\rbrack}}},$while for pixels that do not conform to this model, a value of zerocorresponding to an MR-inactive tissue, is assumed.

Next, a model-conforming Q-MRI algorithm used for the generation of T2quantitative images is presented. The following embodiment of amodel-conforming Q-MRI algorithm for the tissue property T2 uses twosource images as input, specifically IR2_E1 image 260, and IR2_E2 image276, which represent two consecutive measurements at times TE1eff andTE2eff respectively (see Table 1) during the T2 decay of the tissuesignals. $\begin{matrix}{{T2}_{({i,j})} = \left\{ \begin{matrix}{{0\overset{if}{\longleftarrow}{{IR2\_ E1}_{({i,j})}}} \leq {noise}} \\{{0\overset{if}{\longleftarrow}{{IR2\_ E2}_{({i,j})}}} = 0} \\{{{T2}_{water}\overset{if}{\longleftarrow}{{{{IR1\_ E1}_{({i,j})}} - {{IR2\_ E1}_{({i,j})}}}}} \leq {{noise}/4}} \\{\frac{{TE2eff} - {TE1eff}}{\ln\left\lbrack \frac{{IR2\_ E1}_{({i,j})}}{{IR2\_ E2}_{({i,j})}} \right\rbrack}\overset{otherwise}{\longleftarrow}{\begin{matrix}{{For}\quad{pixels}\quad\left( {i,j} \right)\quad{where}} \\{{physics}\quad{model}\quad{is}\quad{valid}}\end{matrix}}}\end{matrix} \right.} & \left\lbrack {{Eq}.\quad 12} \right\rbrack\end{matrix}$

This algorithm starts with three conditional steps that are used toidentify the nonconforming pixels according to the following criteria. AT2 value of zero corresponding to MR-inactive tissues (e.g. corticalbone, air, etc.) is assigned to all pixels were signal in image IR2_E1image 260 is less than the noise and also were the signal of the secondecho (IR2_E2 image 276 ) is identical to zero. Furthermore, in the thirdconditional step, pixels that do not exhibit a measurable T2 decay areassigned the highest possible T2 value, specifically that of pure waterT2 _(water)=2100 ms. In the fourth and final step of this exemplaryembodiment of a model-conforming algorithm, the T2 values for theremaining model-conforming pixels are computed with a standardmono-exponential model for T2 decay, as above discussed in the“Theoretic background” section of this chapter.

When tested experimentally with a phantom and in the human brainsignificant image quality improvements are observed, with respect tobackground noise and geometrical definition of small or thin structurescan be obtained by implementing model-conforming criteria to otherwisestandard Q-MRI algorithms. The model conforming images for T1 and T2were calculated with the following variants of Eq. 10:

Also quantitative accuracy possible with these two model-conformingQ-MRI algorithms was assessed by means experiments with a phantom withknown geometry and relaxation times.

Virtual MRI Scanning Phase

As comprehensive as an MRI examination may be in terms of the specificnumber of individual tissue property weightings used for scanning,relying exclusively on fixed-intrinsic-contrast images for theassessment of disease by MR imaging is not ideal primarily because thefull intrinsic contrast dynamic range (CDR) of any of the weightingtissue properties (e.g. T1, T2, T2*, state of motion, etc.) that can beexplored with MRI, is not necessarily intuitive to the observer apriori. In other words, because only a discrete number of image contrasttypes are used in the detection and the characterization of pathologicentities that in general can have unpredictable values of the weightingtissue properties, the maximum possible sensitivity and specificity ofthe MRI examination might not be achieved. Pathologic entities with ahigher probability of failed detection or characterization with fixedcontrast MR imaging are small sub-voxel size pathologic structures thecontrast of which can be diminished by partial volume averaging, as wellas larger structures exhibiting proton density and relaxation timessimilar in value to that of the surrounding tissues. Of diagnosticimportance is the visualization of entities that can alter patientmanagement, for example subtle tumor invasions to adjacent tissue layersand the detection of focal pathology when surrounded by diffusepathology.

For such applications where the diagnostic information may be containedin a narrow contrast range and therefore may not be revealed withfixed-intrinsic-contrast acquisitions, the development of MR imagingtechniques of the present invention for exploring of the full CDR of therelevant tissues increases the diagnostic power (sensitivity andspecificity) of MR imaging.

One approach that could be instrumental for extracting and forvisualizing the full CDR that is latent in a physically acquired MRimage set can be found in methods stemming from an intricate andmulti-procedural MR imaging concept, which has been referred to by someauthors, generically and as a whole, as MR image synthesis. Imagingtechniques embodying the MR image synthesis concept allow for thecontinuous and on-demand generation of images with computer-synthesizedMR contrast. This can be done subsequently to having physically scannedthe patient by means of specialized (physical) MRI pulse sequences andmost importantly, this image synthesis phase can be performed post factoin the patient's absence by means of a computer program. Based on itsfunction, this computational phase that embodies the laws of MR imagingphysics may be appropriately referred to as virtual MRI scanning. Thepresent invention gives much improved virtual MRI scanning.

For every pixel (i,j), analytic PD generation algorithms can berepresented symbolically by the general formula: $\begin{matrix}{{Analytic\_ PD}_{({i,j})} = \frac{{SI}_{({i,j})}^{m}}{{PSw}\left\lbrack {\left\{ {{TE},{TR},{FA},\quad\ldots}\quad \right\}_{m};\quad\left\{ {{T1}_{({i,j})},{T2}_{({i,j})},\quad\ldots}\quad \right\}} \right\rbrack}} & \left\lbrack {{Eq}.\quad 13} \right\rbrack\end{matrix}$

In this formula, PSw[{TE, TR, FA, . . . }_(m); {T1 _((i,j)), T2_((i,j)), . . . }] is the MR theory-derived pulse sequence weightingfunction evaluated at the pulse sequence settings {TE, TR, FA, . . .}_(m) used to acquire the m^(th) source image SI_((i,j)) ^(m) and alsoevaluated at the relaxation times {T1 _((i,j)), T2 _((i,j)), . . . }that were generated by Q-MRI methods and therefore are not error free.Analytic extrapolation algorithms in this category have been used in oneform or another in all previous physical-virtual MRI investigations,mostly using pulse sequence weighting functions that model the MR signalof conventional pulse sequences such as spin-echo and gradient-echosequences. Analytic extrapolation algorithms are not ideal because theserecycle imperfect image information {T_((i,j)), T2 _((i,j)), . . . }that is incomplete as a consequence of irreversible information lossesthat occurred in prior or intermediate Q-MRI computational steps. Forexample, those steps that were used first to generate the input T1 andT2 data use data having experimental uncertainties. Therefore, whenanalytically extrapolated quantitative PD images are used as the baselevel image set, or equivalently as the virtual patient with the purposeof virtual MRI scanning, synthetic images with reduced SNR and increasedartifact appearance (e.g. pixel dropouts) can result.

In order to avoid these undesirable effects on synthetic image qualityas generated by previously studied physical-virtual MRI scanningmethods, the present inventive method was developed.

Contrast series of synthetic MR images with selected levels of T1 and T2weightings, and with a consistently high image quality level, areproduced by using PD images generated by means of any of the LCSIalgorithms described above. These series of synthetic images aregenerated by means of contrast synthesis algorithms or virtual MRI pulsesequences, which are based on the laws of magnetization-dynamics physics(e.g. Bloch-Torrey theory: a) Bloch F. Nuclear induction. Phys. Rev.70:460-74, 1946 and b) Torrey H C. Bloch equations with diffusion terms.Phys. Rev. 104(3):563-5, 1956.)

The general formula for the generation of synthetic imagesSynthetic_I_((i,j)) with any given virtual MRI pulse sequence that isrepresented by a specific pulse sequence-weighting factor PSw is:Synthetic_(—) I _((i,j)) =LCSI _(—) PD _((i,j)) ·PSw[{TE, TR, FA, . . .} _(m) ; {T 1 _((i,j)) , T2 _((i,j)), . . . }]  [Eq. 14]

Depending on the specific form of the pulse sequence-weighting factor,the formula above can be used to generate synthetic images simulatingcurrently achievable imaging conditions as well as conditions thatcannot be implemented currently due to technological and/or physicallimitations. Important examples of currently achievable imagingconditions include scanning with the conventional spin-echo (CSE) pulsesequence, which is represented by the following pulse sequence weightingfunction: $\begin{matrix}{{{PSw}\left\lbrack {\left\{ {{TE},{TR},{FA},\ldots} \right\}_{m};\left\{ {{T1}_{({i,j})},{T2}_{({i,j})},\ldots} \right\}} \right\rbrack} = {{\sin({FA})}{\exp\left\lbrack {- \frac{TE}{{T2}_{({i,j})}}} \right\rbrack}\left\{ \frac{1 - {\exp\left\lbrack {- \frac{TR}{{T1}_{({i,j})}}} \right\rbrack}}{1 - {{\cos({FA})}{\exp\left\lbrack {- \frac{TR}{{T1}_{({i,j})}}} \right\rbrack}}} \right\}}} & \left\lbrack {{Eq}.\quad 15} \right\rbrack\end{matrix}$Also of practical importance is imaging with the inversion recoveryconventional spin-echo (IR-CSE) pulse sequence that is represented by:$\begin{matrix}{{{PSw}\left\lbrack {\left\{ {{TE},{TR},{FA},\ldots} \right\}_{m};\left\{ {{T1}_{({i,j})},{T2}_{({i,j})},\ldots} \right\}} \right\rbrack} = {{\sin({FA})}{{\exp\left\lbrack {- \frac{TE}{{T2}_{({i,j})}}} \right\rbrack}\left\lbrack {1 - {2{\exp\left\lbrack {- \frac{T1}{{T1}_{({i,j})}}} \right\rbrack}} + {\exp\left\lbrack {- \frac{TR}{{T1}_{({i,j})}}} \right\rbrack}} \right\rbrack}}} & \left\lbrack {{Eq}.\quad 16} \right\rbrack\end{matrix}$

Among the scanning conditions that are not currently achievable by meansof physical MRI scanning and that could be of practical importance are:

1) The possibility of applying repeatedly virtual inversion recoverypulse sequences with different inversion times each chosen to null thesignal from a different tissue. In this way nullifying successively allother tissues may be used as a method for segmentation of any selectedtissue. Theoretically, such a sequential segmentation process may beused for extracting the full CDR latent in the source images extractedby virtual MRI scanning.

2) The generation of nonstandard contrast weightings such as simulated“T1-decay” by replacing T2 _((i,j)) by T1 _((i,j)) in equations 12, 13,or 14 above, and simulated “sum T1+T2” contrast again by replacing T2_((i,j)) by T1 _((i,j))+T2 _((i,j)) in equations 12, 13, or 14.

Flow Diagram of the Invention

Referring again to FIG. 3, a flow diagram 300 is shown. At block 302 thephysical scan is performed to produce four (4) source images, the IR1_E1image 224, the IR1_E2 image 234, the IR2_E1 image 258, and the IR2_E2image 276. From block 302 the process goes to both block 304 and block310.

At block 304, the linear combination of images calculation for a protondensity image is performed. For example, the linear combination ofimages, which generates the maximum signal to noise ratio image, may beutilized. Alternatively, other linear combinations of images may beutilized to produce desired results. After completing block 304 thecalculational procedure goes to block 306.

At block 306, the quantitative proton density image is computed, forexample, using equation 7, in combination with equation 8 and equation 9to calculate the linear combination coefficients. After completing thecalculations of block 306, the calculational procedure goes to block308.

At block 308 the calculational procedure uses the result of Block 306and the results of the calculation using blocks 310 and 312, in order tocompute a desired simulated Magnetic Residence Image Pulse Sequence.

Returning now to block 302, following the acquisition of the sourceimages, the calculational procedure goes to block 310, in addition tothe previously described calculation at block 304.

At block 310 the model-conforming Q_MRI methods are used utilizing theabove-mentioned equations. Following the calculation of block 310, thecalculational procedure goes to block 312.

At block 312, the Q_MR images are used to compute the weighting tissueproperties such as longitudinal relaxation time T1, transverserelaxation time T2, and possibly other tissue properties of interest.For example, in an exemplary embodiment of the invention, thelongitudinal relaxation time T1 is computed at each pixel using Equation11. Also, the transverse relaxation time T2 is computed at each pixelusing equation 12.

Returning to block 308, the quantitative proton density image along withthe tissue properties such as the longitudinal relaxation time T1 andthe transverse relaxation time T2 are used to compute simulated MRimaging pulse sequences. Following the computation of block 308 thecalculational procedure goes to block 320, at which the contrast imageis computed. The contrast image is then presented on a computer screenfor observation by a physician, is printed photographically or by acomputer printer, etc.

Prior Art

Turning now to FIG. 4 a calculational scheme 400 of the prior art isshown. At block 402 the four (4) source images are obtained as at block302. From block 402 the calculational procedure goes to block 410.

At block 410 the calculations done at block 310 are performed. Followingthe calculations of block 410 the calculational procedure goes to block412. At block 412 the calculations preformed at block 312 are performed.Following the calculations at block 412 the calculational procedure goesto block 415 and to block 419.

At block 415 a proton density image is computed using the output of theQ_MR image calculation of block 412. Following the calculation of block415, the calculational procedure goes to block 417 where a protondensity image is computed. Following the calculation of block 417 thecalculational procedure goes to block 419.

At block 419 a virtual MR imaging pulse sequence is computed in responseto the results computed at block 412 and at block 417. Following thecalculation at block 419, the calculational procedure goes to block 421.

At block 421 a synthetic MR image is presented on a computer screen forobservation by a physician, is printed photographically or by a computerprinter, etc.

The difference between the prior art calculation of FIG. 4 and theinventive calculation of FIG. 3 is shown by the use of the linearcombination of scanned images at block 304 and block 306 in order togenerate the quantitative proton density image. Use of the linearcombination of scanned images method produces a proton density imagewith less noise than does the prior art method. This better protondensity image permits calculation of an improved synthetic MR image atblock 320.

Example Images

Turning now to FIG. 5, FIG. 6, FIG. 7, and FIG. 8, the four (4) sourceimages taken by the pulse sequence shown in FIG. 2A, and acquired in thecalculational procedure of FIG. 3 at 302 or acquired by thecalculational procedure of FIG. 4 at block 402 are shown.

FIG. 5 shows the image taken at time 226, the IR1_E1 image, which isregarded as the T1 weighted image.

At FIG. 6 the image taken at time 236, the IR1_E2 image, is shown. TheIR1_E2 image is the T1&T2 weighted image.

FIG. 7 shows the image taken at time 256 and is the IR2_E1 image, and isthe proton density weighted, or PD-weighted image.

FIG. 8 shows the image taken at time 272 and is the IR2_E2 image. TheIR2_E2 image is the image referred to as the proton density and T2weighted image, PD&T2 weighted image.

During acquisition of the images, such as the images of FIG. 5, FIG. 6,FIG. 7, and FIG. 8, a sequence of slices is taken throughout thepatient's body, the patient's head in the example. These slices can bereconstructed along different planes to show regions of interest in thepatient's brain.

Turning now to FIG. 9, an axial orthogonal reconstruction at the midlevel of the patient's brain, and showing the eyes is shown. The imageof FIG. 9 is reconstructed using the inventive calculational procedureshown in FIG. 4 and described with reference to the equation 3 throughequation 15.

Turning now to FIG. 10, a sagittal orthogonal reconstruction showing thepatient's brain as computed using the inventive calculational procedureof FIG. 3 is shown.

Turning now to FIG. 11A-FIG. 11H, a sequence of synthetic images of thebrain are shown. The images are obtained by using the relaxation timesT1 and T2 along with the proton density image computed using theinventive calculational procedure of FIG. 3. The sequence in FIG.11A-FIG. 11H shows the effect of changing the inversion waiting timeinvT 212 on the reconstruction process. The synthetic images of FIG.11A-FIG. 11H are shown as follows: at FIG. 11A the inversion waitingtime 212 is taken as 0. At FIG. 11B the inversion waiting time 212 istaken as 150 milliseconds. At FIG. 11C the inversion waiting time 212 istaken as 300 milliseconds. At FIG. 11D the inversion waiting time 212 istaken as 450 milliseconds. At FIG. 11E the inversion waiting time 212 isis taken as 600 milliseconds. At FIG. 11F the inversion waiting time 212is taken as 750 milliseconds. At FIG. 11G the inversion waiting time 212is taken as 1,500 milliseconds. At FIG. 11H the inversion waiting time212 is taken as 2,500 milliseconds. As can be seen from inspection ofthe images of FIG. 11A-FIG. 11H the distortion of the images by noise isminimal, and the response of the images to different inversion timesinvT 212 is shown.

Turning now to FIG. 12A-FIG. 12H the effect on synthetic images of thebrain obtained by changing the spin echo weighting times TE1 220, 254and TE2 230, 270 is shown. The synthetic images computed by theinventive computational scheme at FIG. 12A shows the effect of using anecho waiting time of 0. At FIG. 12B the image using a spin echo time of10 milliseconds is shown. At FIG. 12C the image obtained using a spinecho time of 15 milliseconds is shown. At FIG. 12D an image using a spinecho time of 30 milliseconds is shown. At FIG. 12E an image using a spinecho time of 60 milliseconds is shown. At FIG. 12F an image using a spinecho time of 90 milliseconds is shown. At FIG. 12G an image using a spinecho time of 120 milliseconds is shown. At FIG. 12H an image using aspin echo time of 200 milliseconds is shown. Examination of the imagesshown in FIG. 12A-FIG. 12H shows that the reconstructed images producedby the novel computational theme at block 302 are clear andsubstantially free of excessive noise. Further, the sequence ofreconstructed images shows the effect of varying the spin echo waitingtime TE1 220, 254, and TE2 230, 270. That is, the reconstructed imagesshow the effect that taking a series of images of the patient atdifferent spin echo-waiting times would produce.

FIG. 11A-FIG. 11H and FIG. 12A-FIG. 12H are reconstructed showingdifferent parameter settings for a magnetic resonance image scanner, andall are computed using a set of four (4) images obtained as shown in thepulse sequence of FIG. 2, and as are illustrated for an exemplaryembodiment of the invention in FIG. 5-FIG. 8.

Turning now to FIG. 13, a control system 13,000 for a magnetic resonanceimagining scanner is shown. The longitudinal magnetic field coil 106 isnot shown in FIG. 13 as ordinarily the longitudinal magnetic field ismaintained at a constant value during the course of a scan, and FIG. 13represents an exemplary control system for controlling hardware during ascan.

The gradient coils are shown, with the X gradient coil 13,002A and13,002B connected by connection 13,004 to gradient drive circuits13,006. The Y gradient coils 13,010A and 13,010B are connected byconnection 13,012 to gradient drive circuits 13,006. Likewise, the Zgradient coils 13,014A and 13,014B are connected by connection 13,016 togradient drive circuits 13,006. Gradient drive circuits 13,006 areconnected to gradient control interface 13,020. The magnetic gradientcoils are used to apply a desired value of magnetic field to a desiredvoxel of the patient's tissue.

Transmitter coil 150, as shown in FIG. 1, is connected to transmitter13,024. Transmitter 13,024 is connected to transmitter control interface13,026.

Radio frequency receiver coil 152, as shown in FIG. 1, is connected toreceiver 13,030. Receiver 13,030 is connected to receiver controlinterface 13,032.

Transmitter control interface 13,026, gradient control interface 13,020,and receiver control interface 13,032 are connect to scan interface13,034. Scan interface 13,034 is connected to computer bus 13,022.

Computer bus 13,022 is a data pathway connecting the control interface13,026 and 13,020 and 13,032 to the other components of a computer. Theother components of a computer comprises, for example, as follows.Central processor unit (CPU) 13,050 controls operation of MRI scanner13,000.

Memory unit 13,052 connects to computer bus 13,022, and contains memoryfor computer programs which execute on CPU 13,050 and the data theprograms work with. The LCSI module 13,053 storing the computer programsof the present invention is shown in memory 13,052.

Disk storage unit 13,057 provides additional storage for data andimages.

Computer terminal 13,054, with monitor screen 13,055, and with keyboard13,056 connects to computer bus 13,022.

Display unit 13,060 provides a high quality display for presenting theimages obtained from patient 102 by the magnetic resonance imagingscanning process. Display 13,060 connects to computer bus 13,022.

Printer 13,062 also connects to computer bus 13,022 and provides a meansfor printing pictures of the images obtained by the magnetic resonanceimaging scanner.

Network interface 13,070 connects to computer bus 13,022, and alsoprovides connection to computer network 13,072.

In operation, magnetic resonance image scanner 100, and as shown withcontrol system 13,000, is controlled by CPU 13,050.

In the exemplary embodiment of the invention shown in FIG. 13, scaninterface 13,034 receives a command from CPU 13,050 to start a scan.Scan interface 13,034 controls the details of executing the scan. Forexample, scan interface 13,034 executes the pulse and scanning sequencedescribed in connection with the exemplary pulse sequence of FIG. 2A.Scan interface 13,034 controls various components of the hardware, forexample: scan interface 13,034 uses the transmitter control interface13,026 to control the radio frequency transmitter 13,024; scan interface13,034 uses gradient control interface face to control the magneticfield gradient 13,006; and, scan interface 13,034 uses receiver controlinterface 13,032 to control radio frequency receiver 13,030. Forexample, scan interface 13,034 may contain a processor to control thevarious interfaces connected thereto, in order to control the magneticfield, radio frequency transmission, and radio frequency reception,during the course of a scan.

CPU 13,050 also provides processing power to analyze image data obtainedfrom the MRI scanner. The images are stored in memory 13,052 and on disk13,057. The equations necessary to generate an image from the dataacquired from radio frequency pickup coil 152 and receiver 13,030 aresolved by CPU 13,050. The finished images are then stored in memory13,052 and disk 13,057 by CPU 13,050. For example, the images shown asFIG. 5-FIG. 12 h are generated by data sent to memory 13,052, byreceiver 13,030. That data then is converted into an image by CPU 13,050and the images are stored into memory 13,052. LCSI module 13,053 storesthe computer program for solving the equations of the invention asdescribed hereinabove, and may, in an exemplary embodiment of theinvention hold the images in appropriate data structures.

Terminal 13,054, and keyboard 13,056 provide a means for an operator tointerface with the computer and MRI system. Display 13,060 is a highquality display which provides a means for presenting images generatedby CPU 13,050 from the data received from receiver 13,030.

Printer 13,062 provides a means for printing images in a paper orphotographic form.

Network interface 13,070 connects the computer system to a computernetwork 13,072 for transfer of information, images, etc., between MRIsystem 13,000 and other systems connected to computer network 13,072.

For example, the computer program used to solve the equations of thepresent invention may be loaded into memory 13,052 by being downloadedthrough computer network 13,072. Alternatively, disk unit 13,057 maycontain a floppy disk unit, or a CD disk unit, and the computer programfor practice of the present invention may be loaded from such a portablecomputer readable media.

It is to be understood that the above-described embodiments are simplyillustrative of the principles of the invention. Various othermodifications and changes may be made by those skilled in the art whichembody the principles of the invention and fall within the spirit andscope thereof.

1. A magnetic resonance imaging scanner, comprising: a longitudinalmagnetic field coil applying a longitudinal magnetic field to a patient;at least one gradient magnetic field coil applying a magnetic fieldgradient to said patient; a radio frequency transmitter applying radiofrequency electromagnetic energy to said patient; a radio frequencyreceiver coil connected to a radio frequency receiver receiving radiofrequency electromagnetic emissions from tissue of said patient; controlcircuits applying a desired pulse sequence of electromagnetic pulses andmagnetic field gradients to said patient in order to generate data fromwhich an image of said patient may be constructed; a memory storing saiddata and storing a computer program; a CPU executing said computerprogram, said computer program analyzing said data by performing thefollowing steps, a. acquiring a plurality of images by said magneticresonance imaging scanner using a predefined pulse sequence; b. forminga linear combination of said plurality of images, said linearcombination formed by summing a product of a coefficient and an image ofsaid plurality of images in order to form a sum of coefficients andimages; c. evaluating said coefficients in order to achieve a desiredeffect on said image in order to give said coefficients a specificnumerical value; and, d. synthesizing a desired image using said linearcombination of said plurality of images and said specific numericalvalue of each coefficient.
 2. The apparatus as in claim 1 wherein saidcomputer program further comprises: steps maximizing a signal to noiseratio in a chosen image.
 3. The apparatus as in claim 1 wherein saidcomputer program further comprises: steps minimizing pixel-by-pixeldifferences in an image.
 4. The apparatus as in claim 1 wherein saidcomputer program further comprises: steps maximizing a signal to noiseratio in a chosen image and simultaneously minimizing pixel-by-pixeldifferences within an image.
 5. The apparatus as in claim 1 wherein saidcomputer program further comprises: first steps computing tissue valuesof model parameters on a pixel by pixel basis; and, second steps inorder to set the tissue value to a predetermined value in response to ameasured value of the image giving a calculated value within a specifiedrange of noise value of the image.
 6. The apparatus as in claim 1wherein said computer program further comprises performing the steps of:computing a tissue value of model parameters on a pixel-by-pixel basis;computing a noise value from said plurality of images; and setting atissue value of a particular pixel to a predetermined value in responseto said tissue value of said particular pixel being within a specifiedrange of said noise value.
 7. Electromagnetic signals traveling on acomputer network, comprising: said electromagnetic signals carryinginstructions enabling the practice of the computer program of claim 1.8. Computer readable media, comprising: said computer readable mediacontaining instructions enabling the practice of the computer program ofclaim
 1. 9. A magnetic resonance imaging scanner, comprising: alongitudinal magnetic field coil applying a longitudinal magnetic fieldto a patient; at least one gradient magnetic field coil applying amagnetic field gradient to said patient; a radio frequency transmitterapplying radio frequency electromagnetic energy to said patient; a radiofrequency receiver coil connected to a radio frequency receiverreceiving radio frequency electromagnetic emissions from tissue of saidpatient; control circuits applying a desired pulse sequence ofelectromagnetic pulses and magnetic field gradients to said patient inorder to generate data from which an image of said patient may beconstructed; a memory storing said data and storing a computer program;a CPU executing said computer program, said computer program analyzingsaid data by performing the following steps, a. acquiring a plurality ofimages by said magnetic resonance imaging scanner using a predefinedpulse sequence; b. forming a linear combination of said plurality ofimages, said linear combination formed by summing a product of acoefficient and an image of said plurality of images in order to form asum of coefficients and images; c. evaluating said coefficients in orderto achieve a desired effect on said image by giving said coefficients aspecific numerical value; and, d. synthesizing a desired image usingsaid linear combination of said plurality of images and said specificnumerical value of each coefficient, wherein said computer program, e.computes tissue values of model parameters on a pixel-by-pixel basis; f.sets the tissue value to a predetermined value in response to a measuredvalue of the image giving a calculated value within a specified range ofnoise value of the image; and g. sets a value of T1 to zero in the eventthat an image value in a pixel is less than a noise value.
 10. Amagnetic resonance imaging scanner, comprising: a longitudinal magneticfield coil applying a longitudinal magnetic field to a patient; at leastone gradient magnetic field coil applying a magnetic field gradient tosaid patient; a radio frequency transmitter applying radio frequencyelectromagnetic energy to said patient; a radio frequency receiver coilconnected to a radio frequency receiver receiving radio frequencyelectromagnetic emissions from tissue of said patient; control circuitsapplying a desired pulse sequence of electromagnetic pulses and magneticfield gradients to said patient in order to generate data from which animage of said patient may be constructed; a memory storing said data andstoring a computer program; a CPU executing said computer program, saidcomputer program analyzing said data by performing the following steps,a. acquiring a plurality of images by said magnetic resonance imagingscanner using a predefined pulse sequence; b. forming a linearcombination of said plurality of images, said linear combination formedby summing a product of a coefficient and an image of said plurality ofimages in order to form a sum of coefficients and images; c. evaluatingsaid coefficient in order to achieve a desired effect on said image bygiving said coefficients a specific numerical value; and, d.synthesizing a desired image using said linear combination of saidplurality of images and said specific numerical value of eachcoefficient, wherein said computer program, e. computes tissue values ofmodel parameters on a pixel-by-pixel basis; f. sets the tissue value toa predetermined value in response to a measured value of the imagegiving a calculated value within a specified range of noise value of theimage; and g. sets a value of T2 equal to zero in the event that a pixelvalue in an image is less than a noise value for that pixel.
 11. Amagnetic resonance imaging scanner, comprising: a longitudinal magneticfield coil applying a longitudinal magnetic field to a patient; at leastone gradient magnetic field coil applying a magnetic field gradient tosaid patient; a radio frequency transmitter applying radio frequencyelectromagnetic energy to said patient; a radio frequency receiver coilconnected to a radio frequency receiver receiving radio frequencyelectromagnetic emissions from tissue of said patient; control circuitsapplying a desired pulse sequence of electromagnetic pulses and magneticfield gradients to said patient in order to generate data from which animage of said patient may be constructed; a memory storing said data andstoring a computer program; a CPU executing said computer program, saidcomputer program analyzing said data by performing the following steps,a. acquiring a plurality of images by said magnetic resonance imagingscanner using a predefined pulse sequence; b. forming a linearcombination of said plurality of images, said linear combination formedby summing a product of a coefficient and an image of said plurality ofimages in order to form a sum of coefficients and images; c. evaluatingsaid coefficients in order to achieve a desired effect on said image bygiving to give said coefficients a specific numerical value; and, d.synthesizing a desired image using said linear combination of saidplurality of images and said specific numerical value of eachcoefficient, wherein said computer program, e. computes tissue values ofmodel parameters on a pixel-by-pixel basis; f. sets the tissue value toa predetermined value in response to a measured value of the imagegiving a calculated value within a specified range of noise value of theimage; and g. sets a value of T2 equal to the value of T2 for water fora pixel, in the event that for said pixel the computed image value:IR1_EI−IR2_E1 is less than a noise value for said pixel.
 12. A magneticresonance imaging scanner, comprising: a longitudinal magnetic fieldcoil applying a longitudinal magnetic field to a patient; at least onegradient magnetic field coil applying a magnetic field gradient to saidpatient; a radio frequency transmitter applying radio frequencyelectromagnetic energy to said patient; a radio frequency receiver coilconnected to a radio frequency receiver receiving radio frequencyelectromagnetic emissions from tissue of said patient; control circuitsapplying a desired pulse sequence of electromagnetic pulses and magneticfield gradients to said patient in order to generate data from which animage of said patient may be constructed; a memory storing said data andstoring a computer program; a CPU executing said computer program, saidcomputer program analyzing said data by performing the following steps,a. acquiring a plurality of images by said magnetic resonance imagingscanner using a predefined pulse sequence; b. forming a linearcombination of said plurality of images, said linear combination formedby summing a product of a coefficient and an image of said plurality ofimages in order to form a sum of coefficients and images; c. evaluatingsaid coefficients in order to achieve a desired effect on said image bygiving said coefficients a specific numerical value; d. synthesizing adesired image using said linear combination of said plurality of imagesand said specific numerical value of each coefficient; e. said computerprogram, e.1 computing on a pixel-by-pixel basis the values ofquantitative tissue parameters using an MR physics model; e.2 computingnoise levels from said plurality of images in order to obtain measurednoise levels; e.3 executing a conditional statement, said conditionalstatement comparing a parameter computed from said quantitative tissueparameters with said measured noise levels; e.4 setting, in response tosaid executed conditional statement generating a first result, an imagevalue in a particular pixel equal to a value computed from said MRphysics model; e.5 setting, in response to said executed conditionalstatement generating a second result, an image value in a particularpixel equal to a predetermined value.
 13. The apparatus as in claim 12wherein said computer program further comprises performing the steps of:executing a further conditional statement, said further conditionalstatement comparing a further parameter computed from said quantitativetissue parameters with said measured noise levels; setting, in responseto said executed conditional statement and said executed furtherconditional statement generating a first result, an image value in aparticular pixel equal to a value computed from said MR physics model;setting, in response to said executed conditional statement and saidexecuted further conditional statement generating a second result, animage value in a particular pixel equal to a predetermined value. 14.The apparatus as in claim 12 further comprising the steps of: selectingas said a predefined pulse sequence a mixed turbo spin echo pulsesequence (mix-TSE pulse sequence); acquiring as said plurality of imagesa IR1_E1 image, a IR1_E2 image, a IR2_E1 image, and a IR2_E2 image;measuring noise levels from said plurality of images; computing a valueof T1 at each pixel using said plurality of images; computing a valuefor T1 at a pixel, in the event that said executed conditional statementhas said first result, using the expression,T 1=Ln(½(1−(IR 1 _(—) E 1)/(IR 2 _(—) E 1)) ) utilizing as a value ofsaid predetermined constant the value of zero (0) for T1 in a pixel. 15.The apparatus as in claim 12 wherein said computer program furthercomprises executing the step of: utilizing as a value for T1 in saidpixel the value of said predetermined constant, in the event that anexecuted further conditional statement has a third value.
 16. Theapparatus as in claim 12 further comprising the steps of: selecting assaid predefined pulse sequence a mixed turbo spin echo pulse sequence(mix-TSE pulse sequence); acquiring as said plurality of images a IR1_E1image, a IR1_E2 image, a IR2_E1 image, and a IR2_E2 image; measuringnoise levels from said plurality of images; computing a value of T2 ateach pixel using said plurality of images; utilizing as a value of saidpredetermined constant, the value of T2 for pure water.
 17. Theapparatus as in claim 16 wherein said computer program further comprisesexecuting the step of: utilizing as said value of T2 for pure water thevalue of 2100 milliseconds.
 18. The apparatus as in claim 12 whereinsaid computer program further comprises executing the step of: utilizingas a value for T2 in said pixel the value of said predeterminedconstant, in the event that an executed further conditional statementhas a third value.
 19. The apparatus as in claim 12 wherein saidcomputer program further comprises executing the step of: giving saidexecuted conditional statement said second result when an, absolutevalue (IR2_E1)<=noise.
 20. The apparatus as in claim 12 wherein saidcomputer program further comprises executing the step of: giving saidexecuted conditional statement said second result when an, absolutevalue (IR2_E2)=0.
 21. The apparatus as in claim 12 wherein said computerprogram further comprises executing the steps of: giving said executedconditional statement said second result when an absolute value(absolute value (IR1_E1) absolute value (IR2_E1))<=noise/4.
 22. Theapparatus as in claim 12 wherein said computer program further comprisesexecuting the step of: computing the value of T2 in said pixel, whensaid executed conditional statement has said first result, using theexpression,T 2=Ln((IR 2 E 1)/(IR 2 E 2)), as shown in equation 12 of thedisclosure.
 23. The apparatus as in claim 12 wherein said computerprogram further comprises executing the step of: computing, in responseto said sequence of acquired images, a synthesized image based on afurther pulse sequence, said further pulse sequence differing from saidpredefined pulse sequence.
 24. The apparatus as in claim 12 wherein saidcomputer program further comprises performing the steps of: selectingsaid quantitative tissue parameters as T1 values at each pixel; andselecting said predetermined value as a constant.
 25. The apparatus asin claim 12 wherein said computer program further comprises performingthe steps of: selecting said quantitative tissue parameters as T2 valuesat each pixel; and selecting said predetermined value as a constant. 26.The apparatus as in claim 25 wherein said computer program furthercomprises performing the step of: selecting said predetermined value asa T2 value of pure water.